January 24, 2005
Starting Valuations Matter
Let's do a little experiment. The results are critical if you want to understand the market here, so even non-mathematical readers are encouraged to spend some time with this update. Calculations are at the bottom of the page if you want some practice.
Consider a stock with earnings of say $10, paying out 40% in dividends and reinvesting what remains to produce long-term earnings growth of 6% annually. Price the stock to deliver a 10% long-term rate of return. On those assumptions, the starting P/E ratio for this stock will be 10.6*
Now let 25 years go by, over which time the valuation of the stock increases smoothly, to the point that it is now priced to deliver only an 8% long-term rate of return. At this point, the stock will have an ending P/E ratio of 21.2**
Here's a crucial result. Even though the stock was initially priced to deliver a long-term rate of return of just 10%, the fact that valuations increased over the holding period means that the actual return over the 25 year holding period was even higher: 12% in fact. Moreover, because the P/E multiple trended higher over time (as the long-term rate of return priced into the stock declined), the average P/E multiple over the full period turns out to be 14.7.
Seeing this, an uninformed investor – looking the data without imposing any structure on it – might be misled into thinking that on average, the P/E on stocks ought to be about 14.7, and that on average, the long-term return on stocks ought to be about 12%. Of course, these inferences are utterly wrong, and are simply artifacts of the gradual rise in valuations over the holding period. If an investor looked more carefully at the source of investment returns, distinguishing returns initially priced into valuations from the returns resulting from a change in valuations, or alternatively, if the investor occasionally took the time to operate a calculator, it would be clear that a P/E of 14.7 actually prices in a long-term total return of just 8.88%***
While the exact numbers in our experiment can be changed somewhat if you wiggle the assumptions about growth rates and payout ratios, the basic result stands: starting valuations matter, and averaging historical P/E multiples and returns over periods of generally rising valuations is a dangerous way to estimate future investment results.
Backing into the P/E multiple
As an alternative way of demonstrating that valuations matter for long-term returns, consider another experiment using actual historical data for the S&P 500. Since we know the actual history of prices and dividends going back more than a century, we can pick any point in time and ask the following question: knowing the future value of the S&P 500 ten years in the future, as well as all the dividends paid on the index, what starting P/E multiple would have been required in order for the S&P 500 to produce a 10% annual total return over the following decade? (As usual, I used price/peak earnings multiples to mute the uninformative effect of earnings swings during recessions, which also increases the consistency of the results over history).
It turns out that historically, in order to provide 10% annual total return over the subsequent decade, the required starting price/peak-earnings multiple on the S&P 500 would have averaged just 13.3. In order to deliver a higher, 12% annual total return over the subsequent decade, the required starting P/E would have averaged just 10.9. In contrast, in order to deliver an annual total return of just 8% over the following decade, the required starting P/E would have averaged 15.9.
All of which is rather uncomfortable given that the S&P 500 currently sports a multiple over 20 times peak earnings, which would be consistent with a 10-year return of about 4% annually.
There's some good news and bad news here. First the good news. Looking at these calculations, it turns out that there have been a few times when very high starting P/E multiples would have still delivered good returns. The main example of this was 1990. Even if investors had paid a P/E multiple of 31 in that year, they still would have earned a 10% annualized rate of return on stocks over the following decade, as the actual P/E multiple on the S&P 500 ended the period at an even higher 34 times peak earnings. Combine that expansion in the P/E multiple with 6% peak-to-peak earnings growth during the 1990's and low but still important dividends, and there's your 10% annual return.
So if investors could rely on current P/E multiples expanding over the coming decade (despite the fact that we've never seen valuations this high except at speculative extremes), it follows that investors might come out with an acceptable total return from a buy-and-hold approach even from current valuations. The real issue is whether investors can reasonably rely on that sort of outcome. I suspect that my own views on that are obvious.
So there's the good news.
The bad news is that even the average starting P/E multiples quoted above were calculated during a period of generally rising valuations. Notice for example that allowing a P/E of 31 in 1990 has the effect of skewing the historical average higher (as a practical matter, so do all the calculations after 1986).
If we recalculate the averages to exclude ending valuations occurring during the recent stock market bubble (which effectively means excluding starting P/E multiples beyond 1986), the results are even more sobering.
On that basis, in order to deliver 10% annualized returns over the subsequent decade, the required starting P/E on the S&P 500 would have historically had to average just 12.2 (just under 13 if one looks only at post-1950 data). In order to deliver a higher, 12% annualized return, the required starting P/E would have averaged just 11.4. Finally, in order to deliver an annualized total return of just 8% over the subsequent decade, the starting P/E on the S&P 500 would have had to average 14.8 (just over 15 if one looks only at post-1950 data).
All of this underscores the fact that in order for stocks to provide a satisfactory long-term return from a buy-and-hold approach, it is not enough to argue that current P/E multiples are justified (e.g. on the basis of current inflation, interest rates, the Fed model, a sweet spot in the economy, and the like). Rather, you have to argue that current P/E multiples are sustainable indefinitely and are, in fact, likely to expand over time from these levels.
Needless to say, since the Hussman Funds are not intended to closely track short-term fluctuations in major indices such as the S&P 500, the Funds are not appropriate vehicles for investors pursuing a buy-and-hold approach toward these indices.
Years ending in “5”
It's unfortunate that serious investors would even entertain superstitions of this type, but with valuations higher than they were at the 1929, 1972 and 1987 market peaks, I suppose that investors have to reach for something. In this case, bullish arguments have increasingly included the observation that there have been no down-years ending in 5 over the past century.
Now, stare at that for a second. Historically, the market has advanced some 70% of the time, declining the other 30%. Over the past century, a year ending in any particular number has had 10 times to show its stuff. So the probability of getting an advancing year 10 times in a row for a year ending in any particular number is just (0.7)^10 = 2.82%. Of course, there are 10 digits that you could end with, so the probability that you would have seen all-advances in at least one of those ending-digits is 1 – (1 –.0282)^10 = 24.9%, which is relatively low, but not strikingly mysterious. Of course, if you mine the historical data a dozen independent ways for patterns like this, each having only a 24.9% chance of showing up, the probability that at least one such pattern will emerge is 1 – (1 – .249)^12 = 96.8%.
In short, if you give me a dozen opportunities to mine the data in ways that have even modest probability of coming up with an interesting superstition, it's almost certain that I'll come up with an interesting superstition.
Notice that this is why you should always be aware of the sample size and the number of groups included in a particular analysis. For example, if every year ending in an even number had been an advancing year over the past century, there would be 50 such events, and the probability of all being advances would be (0.7)^50 = 0.000000018. Even allowing 2 groups (even/odd), and the opportunity to mine the data for thousands of similar relationships, the likelihood of this being a chance outcome would still be nearly zero.
As for years ending in “5,” the statistics are completely unimpressive.
Don't step under any ladders, now.
As of last week, the Market Climate for stocks remained characterized by unusually unfavorable valuations but still tenuously favorable market action. On the negative side, credit spreads have begun to expand, most notably on the junkiest of the junk, but not as clearly on broader corporate debt. Still, it's clear that the markets have finally given up the blind quest for yield – regardless of credit quality. That's something we'll have to keep a very close eye on, because when the market trades at very speculative valuations, as this one does, a reduced willingness of investors to speculate can have fairly abrupt effects.
Still, we haven't observed enough in the way of internal breakdowns to conclude that investors have become generally skittish toward market risk. Odd as it sounds, this has been an impressively well-behaved decline to-date. The number of stocks hitting fresh 52-week lows has remained very limited, overall breadth has been fairly resilient, and we still don't observe enough breakdowns in the action of various industry groups to conclude much in the way of fresh risk-aversion by investors.
Valuations certainly require that we maintain full coverage in terms of downside risk, so the Strategic Growth Fund continues to hold put option coverage with a sufficient notional value to defend the full dollar value of its portfolio holdings against market fluctuations. However, the Fund does not have a corresponding short position in call options (which would effectively convert our directional put protection to a full offsetting short position in the S&P 100 and Russell 2000). As noted last week, our investment position can be viewed either as 1) fully hedged, with the entire value of our stock holdings offset with short positions in the major indices, plus about 1.5% invested in call options, or 2) hedged with put options only.
Either way one looks at it, the difference between our current position and one that was fully hedged amounts to about 1.5% invested in call options. Should the market plunge here, the Fund's performance would be as much as 1.5% lower than it would have been if the Fund was fully hedged. Should the market advance substantially, I would expect the Fund to participate to the extent that our stocks advance, albeit with a modest reduction in performance as a result of the Fund's put option coverage. In effect, the Fund remains constructive toward the market overall, but well hedged against substantial downside risk should it emerge.
In bonds, the Market Climate remains characterized by modestly unfavorable valuations and modestly unfavorable market action, holding the Strategic Total Return Fund to a limited duration of about 2 years (meaning that a 100 basis point change in interest rates would be expected to affect the Fund by about 2% on the basis of bond price fluctuations). The Fund's fixed income positions remain predominantly in Treasury Inflation Protected Securities of moderate duration (generally less than 10-year maturities), as well as in Treasury bill positions. It appears likely that the yield curve will continue to flatten, but the potential for upward bias in yields means that any barbell-type positions are best established at very modest maturities. Overall, I don't view the yield premium on longer-term bonds as justifying the corresponding duration risks. In addition to fixed-income positions, the Strategic Total Return Fund continues to hold about 19% of assets in precious metals shares, which continue to account for most of the day-to-day fluctuation in the Fund.
*Geeks note: This is just the basic dividend discount model. Repeat these calculations as an exercise. k = 0.10, g = .06, E0 = $10, D1 = 0.40x1.06xE0, P0 = D1/k-g = 106, P/E = 10.6
**Same assumptions otherwise, P25 = 909.88 – prove it. Careful: P25 requires D26.
***Prove this to yourself by assuming any level of initial earnings E0 you choose.
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